English

Critical digraphs with few vertices

Combinatorics 2019-10-08 v1

Abstract

We show that every k-dichromatic vertex-critical digraph on at most 2k-2 vertices has a disconnected complement. This answers a question of Bang-Jensen et al., and generalises a classical theorem of Gallai on undirected vertex-critical graphs.

Keywords

Cite

@article{arxiv.1910.02454,
  title  = {Critical digraphs with few vertices},
  author = {Matěj Stehlík},
  journal= {arXiv preprint arXiv:1910.02454},
  year   = {2019}
}
R2 v1 2026-06-23T11:35:39.513Z